Question

A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip. Each small car can hold 5 people and each large car can hold 7 people. A total of 10 cars were rented which can hold 66 people altogether. Write a system of equations that could be used to determine the number of small cars rented and the number of large cars rented. Define the variables that you use to write the system.

Answer 1

A system of equations to determine the number of small and large cars rented would be x + y = 10 and 5x + 7y = 66, where x is the number of small cars and y is the number of large cars.

Step-by-step explanation:

To determine the number of small cars (which can hold 5 people each) and large cars (which can hold 7 people each) rented by the group of college students, we first define our variables:

• Let x be the number of small cars rented.
• Let y be the number of large cars rented.

Now we can write a system of equations based on the information provided:

1. Total number of cars rented: x + y = 10
2. Total capacity of people: 5x + 7y = 66

The first equation comes from the fact that a total of 10 cars were rented, and the second equation reflects the total number of people (66) that can be transported by the cars rented.